Question

9 mark for review a circle has center o, and points r and s lie on the circle. in triangle ors, the measure of ∠ros is 88°. what is the measure of ∠rso, in degrees? (disregard the degree symbol when entering your answer.)

Explanation:

Step1: Identify triangle type

Since \( O \) is the center and \( R, S \) are on the circle, \( OR = OS \) (radii of the circle), so \( \triangle ORS \) is isosceles with \( OR = OS \). Thus, \( \angle ORS=\angle RSO \).

Step2: Use triangle angle sum

The sum of angles in a triangle is \( 180^\circ \). Let \( \angle RSO = x \), then \( \angle ORS = x \) and \( \angle ROS = 88^\circ \). So, \( x + x+ 88^\circ=180^\circ \).

Step3: Solve for \( x \)

Simplify the equation: \( 2x = 180 - 88 \), \( 2x = 92 \), so \( x=\frac{92}{2}=46 \).

Answer:

46